Volker Kauder, leader of Merkel's Christian Democrats (CDU) in parliament, told a party congress he expected a "clear signal" on the issue from the government of Prime Minister Tayyip Erdogan before membership talks could continue.
"A country that wants to be part of Europe must accept the basic principle of religious freedom," he said.
"That means, that we expect Christians in Turkey to be able to build churches without any restrictions, just as Muslims build mosques here in Germany," he said.
Kauder's comments were seen as more of an appeal to members of his party who are skeptical about letting a Muslim-majority country into the EU, rather than an active attempt to block Turkey's membership talks, which are already stalled.
There was no immediate reaction from Ankara. The EU has in the past criticized Turkey's treatment of its Christian minorities, including Greek Orthodox and Armenians.
But recent EU reports on Turkey's accession talks have not referred to any restrictions on building places of Christian worship.
Turkey is a secular republic but most of its 75 million people are Muslim. Religious conservatives and secular opponents vie for public influence and critics accuse the government of Prime Minister Tayyip Erdogan of trying to impose Islamic values by stealth.
Religious conservatives form the bedrock of support for the prime minister's Islamist-rooted AK Party. Secular opponents have cited the lifting of a ban on female students wearing headscarves in religious schools, and the fining of a television channel for airing an episode of "The Simpsons", deemed blasphemous, as evidence of the party's hidden agenda.
Merkel told Erdogan during his visit to Berlin in late October that the EU would pursue accession talks with Turkey in good faith.
But Erdogan said the EU would lose Turkey if it did not grant it membership by 2023. Last month he said his country should consider bringing back the death penalty, a step which would doom the EU bid.
Launched in 2005, the membership talks have stalled due to a dispute over the divided island of Cyprus and skepticism from Merkel and some other European politicians who favor a "privileged partnership" falling short of full membership.
Germany is Turkey's largest trading partner in the EU and is also home to some three million Turks, the largest diaspora in Europe.
(Writing by Noah Barkin, Editing by Gareth Jones and Andrew Heavens)